Title: An introduction to models based on Laguerre, Kautz and other related orthonormal functions – Part II: non-linear models

Authors: Gustavo H.C. Oliveira; Alex Da Rosa; Ricardo J.G.B. Campello; Jeremias B. Machado; Wagner C. Amaral

Addresses: Department of Electrical Engineering, Federal University of Paraná (UFPR), 80215-901, Curitiba-PR, Brazil. ' Department of Electrical Engineering, University of Brasília (UnB), 70910-900, Brasília-DF, Brazil. ' Department of Computer Sciences, University of São Paulo (USP), 13560-970, São Carlos-SP, Brazil. ' Engineering and Information Technology Institute, Federal University of Itajubá (UNIFEI), 37500-903, Itajubá-MG, Brazil. ' School of Electrical and Computer Engineering, University of Campinas (UNICAMP), 13083-852, Campinas-SP, Brazil

Abstract: This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalised orthonormal basis functions. The paper is separated in two parts. The first part of the paper approached issues related with linear models and models with uncertain parameters. Now, the mathematical foundations as well as their advantages and limitations are discussed within the contexts of non-linear system identification. The discussions comprise a broad bibliographical survey of the subject and a comparative analysis involving some specific model realisations, namely, Volterra, fuzzy, and neural models within the orthonormal basis functions framework. Theoretical and practical issues regarding the identification of these non-linear models are presented and illustrated by means of two case studies.

Keywords: modelling; nonlinear system identification; robust identification; Volterra models; orthonormal basis functions; fuzzy models; neural networks.

DOI: 10.1504/IJMIC.2012.046691

International Journal of Modelling, Identification and Control, 2012 Vol.16 No.1, pp.1 - 14

Published online: 17 Dec 2014 *

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